The equation of the circle \( C \) is \( x^{2}+y^{2}-2 x-12 y-252=0 \). Denote the centre of \( C \) by \( G \). The coordinates of the point \( A \) are \( (19,30) \). (a) Find the distance between \( A \) and \( G \). (b) Let \( P \) be moving point in the rectangular coordinate plane such that \( P \) is equidistant from \( A \) and \( G \). Denote the locus of \( P \) by \( \Gamma \). (i) Describe the geometric relationship between \( \Gamma \) and \( A G \). (ii) Suppose \( \Gamma \) cuts \( C \) at the points \( M \) and \( N \). Find the perimeter of \( \triangle A M N \).

If a sphere has a radius of 5 cm, what is its surface area? Use \( S = 4\pi r^{2} \).

The area of a trapezium is 34 cm 2 and the length of one of the parallel sides is 10 cm and ight is 4 cm . Find the length of the other parallel side.

Exercice : \( 2^{2} \) Soit \( A B C \) est un triangle rectangle en \( A \) tels que : \( A B=4 \) et \( A C=4 \sqrt{5} \) 1 Calculer : \( B C \) 2 Calculer : \( \sin \widehat{A B C}, \cos \widehat{A B C} \) et \( \tan \widehat{A B C} \) 3 Soit \( H \) le projeté orthogonal de \( A \) sur \( (B C) \). Calculer : \( A H \)

8. A ship sails 95 km on a bearing of \( 140^{\circ} \), then a further 102 km on a bearing of \( 260^{\circ} \) and then returns directly to its starting point. Find the distance and bearing of the return journey.

In a right triangle, if one angle measures 30 degrees, what is the measure of the other non-right angle?